Related papers: New Geometric Continuity Solution of Parametric Su…
In this paper, Hermite interpolation by parametric spline surfaces on triangulations is considered. The splines interpolate points, the corresponding tangent planes and normal curvature forms at domain vertices and approximate tangent…
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
We introduce a new algorithm to parallelise the computation of persistent homology of 2D alpha complexes. Our algorithm distributes the input point cloud among the cores which then compute a cover based on a rectilinear grid. We show how to…
We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
We present a semi-Lagrangian method for the numerical resolution of Vlasov-type equations on multi-patch meshes. Following N. Crouseilles et al. [A parallel Vlasov solver based on local cubic spline interpolation on patches. Journal of…
Bezier parametric patches are used in engineering practice quite often, especially in CAD/CAM systems oriented to mechanical design. In many cases quadrilateral meshes are used for tessellation of parameters domain. We propose a new…
we consider a system with homoclinic orbit, We decompose the corresponding variational equation on the space of solutions and provide sufficient conditions for the permanency of homoclinic in the space of $C^1$ vector fields. We also…
Spherical functions appear throughout computer graphics, from spherical harmonic lighting and precomputed radiance transfer to neural radiance fields and procedural planet rendering. Efficient evaluation is critical for real-time…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion…
Transfinite patches provide a simple and elegant solution to the problem of representing non-four-sided continuous surfaces, which are useful in a variety of applications, such as curve network based design. Real-time responsiveness is…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…
Isogeometric analysis uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get flexibility…
Defined mathematically as critical points of surface area subject to a volume constraint, constant mean curvatures (CMC) surfaces are idealizations of interfaces occurring between two immiscible fluids. Their behavior elucidates phenomena…
A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
In this paper, we present a new Hermite type curve piecewise polynomial of C1 continuity on nonuniform grids. Depending on the location of the knots of the grid (uniform and nonuniform), the curve is quadratic or cubic. The approximation…